Plane strain propagation of a hydraulic fracture in a permeable rock

Engineering Fracture Mechanics

Volumn 75, Issue 16, 2008, Pages 4666-4694

  Adachi, José I ^a   Detournay, Emmanuel ^b,c  

^a SCHLUMBERGER   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

^c CSIRO   (Australia)

Author keywords

Asymptotic analysis; Hydraulic fracture; Stable crack growth

Indexed keywords

ASYMPTOTIC ANALYSIS; CRACK PROPAGATION; ELASTIC MODULI; FLUID DYNAMICS; FLUID MECHANICS; FRACTURE FIXATION; FRACTURING FLUIDS; HYDRAULIC FRACTURING; HYDRAULICS; INTEGRAL EQUATIONS; LEAKAGE (FLUID); MARKOV PROCESSES; NEWTONIAN LIQUIDS; NUMERICAL METHODS; ROCK MECHANICS; SOLUTIONS;

ASYMPTOTIC BEHAVIORS; ASYMPTOTIC SOLUTIONS; CONSTANT RATES; ENERGY RATES; FAR FIELDS; FLUID FRONTS; FLUID PRESSURES; FRACTURE PROPAGATIONS; HYDRAULIC FRACTURE; INCOMPRESSIBLE NEWTONIAN FLUID; LIMITING CASES; LINEAR ELASTIC MEDIUM; LUBRICATION THEORY; NUMERICAL SOLUTIONS; ONE-DIMENSIONAL DIFFUSION PROCESS; PLANE STRAIN PROBLEMS; PLANE STRAINS; PROPAGATION REGIMES; SINGULAR INTEGRAL EQUATION; STABLE CRACK GROWTH; TIME-MARCHING ALGORITHMS; VISCOUS DISSIPATION;

FRACTURE;

EID: 50249103784     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engfracmech.2008.04.006     Document Type: Article

References (70)

1. Lister J.R. Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors. J Fluid Mech 210 (1990) 263-280
2. Spence D.A., and Turcotte D.L. Magma-driven propagation crack. J Geophys Res 90 (1985) 575-580
3. Jeffrey RG, Settari A, Mills KW, Zhang X, Detournay E. Hydraulic fracturing to induce caving: fracture model development and comparison to field data. In: Elsworth D, Tinucci JP, Heasley KA, editors. Rock mechanics in the national interest - proceedings of the 38th US rock mechanics symposium, vol. 1. Lisse: Balkema; 2001. p. 251-9.
4. Zhang X., Detournay E., and Jeffrey R.G. Propagation of a penny-shaped hydraulic fracture parallel to the free-surface on an elastic half-space. Int J Fract 115 (2002) 125-158
5. Moschovidis Z et al. The Mounds drill-cuttings injection experiment: final results and conclusions. In: Proceedings of the IADC/SPE drilling conference. Richardson: Society of Petroleum Engineers; 2000 [SPE 59115].
6. Frank U., and Barkley N. Remediation of low permeability subsurface formations by fracturing enhancements of soil vapor extraction. J Hazard Mater 40 (2005) 191-201
7. Murdoch L.C. Mechanical analysis of idealized shallow hydraulic fracture. J Geotech Geoenviron 128 (2002) 488-495
8. Murdoch L.C., and Slack W.W. Forms of hydraulic fractures in shallow fine-grained formations. J Geotech Geoenviron 128 (2002) 479-487
9. Haimson B.C., and Lee M.Y. Statistical evaluation of hydraulic fracturing stress measurement parameters. Int J Rock Mech Min Sci Geomech Abstr 26 6 (1989) 447-456
10. Hayashi K., and Haimson B.C. Characteristics of shut-in curves in hydraulic fracturing stress measurements and determination of in situ minimum compressive stress. J Geophys Res 96 B11 (1991) 18311-18321
11. Hayashi K., and Ito T. In situ stress measurement by hydraulic fracturing at the Kamaishi mine. Int J Rock Mech Min Sci Geomech Abstr 30 7 (1993) 951-957
12. Ito T., and Hayashi K. Analysis of crack reopening behavior for hydrofrac stress measurement. Int J Rock Mech Min Sci Geomech Abstr 30 7 (1993) 1235-1240
13. Haimson B.C., Lee M., Chandler N., and Martin D. Estimating the state of stress from subhorizontal hydraulic fractures at the Underground Research Laboratory, Manitoba. Int J Rock Mech Min Sci Geomech Abstr 30 7 (1993) 959-964
14. Desroches J. Stress testing with the micro-hydraulic fracturing technique - focus on fracture reopening. In: Daeman J, Schultz R, editors. Proceedings of the 35th US rock mechanics symposium. Rotterdam: Balkema; 1995. p. 217-23.
15. Haimson B.C., and Cornet F.H. ISRM suggested methods for rock stress estimation - Part 3: hydraulic fracturing (HF) and/or hydraulic testing of pre-existing fractures (HTPF). Int J Rock Mech Min Sci 40 7-8 (2003) 1011-1020
16. Pine RJ, Cundall PA. Applications of the fluid-rock interaction program (FRIP) to the modelling of hot dry rock geothermal energy systems. In: Proceedings of the international symposium on fundamentals of rock joints; 1985. p. 293-302.
17. Evans K.F., Cornet F.H., Hashida T., Hayashi K., Ito T., Matsuki K., et al. Stress and rock mechanics issues of relevance to HDR/HWR engineered geothermal systems: review of developments during the past 15 years. Geothermics 28 4-5 (1999) 455-474
18. Fomin S., Hashida T., Shimizu A., Matsuki K., and Sakaguchi K. Fractal concept in numerical simulation of hydraulic fracturing of the hot dry rock geothermal reservoir. Hydrol Proc 17 14 (2003) 2795-2989
19. Legarth B., Huenges E., and Zimmermann G. Hydraulic fracturing in sedimentary geothermal reservoir: results and implications. Int J Rock Mech Min Sci 42 7-8 (2005) 1028-1041
20. Khristianovic SA, Zheltov YP. Formation of vertical fractures by means of highly viscous fluids. In: Proceedings of the fourth world petroleum congress, vol. II; 1955. p. 579-86.
21. Barenblatt G.I. On the formation of horizontal cracks in hydraulic fracture of an oil-bearing stratum. Prikl Mater Mech 20 (1956) 475-486
22. Hubbert M.K., and Willis D.G. Mechanics of hydraulic fracturing. Trans AIME 210 (1957) 153-168
23. Crittendon B.C. The mechanics of design and interpretation of hydraulic fracture treatments. J Pet Tech (1959)
24. Perkins T.K., and Kern L.R. Widths of hydraulic fractures. J Pet Tech 222 (1961) 937-949 [SPE 89]
25. Geertsma J., and de Klerk F. A rapid method of predicting width and extent of hydraulically induced fractures. J Pet Tech 246 (1969) 1571-1581 [SPE 2458]
26. Nordgren R.P. Propagation of vertical hydraulic fractures. J Pet Tech 253 (1972) 306-314 [SPE 3009]
27. Geertsma J., and Haafkens R. A comparison of the theories for predicting width and extent of vertical hydraulically induced fractures. ASME J Energy Res Tech 101 (1979) 8-19
28. Spence D.A., and Sharp P.W. Self-similar solution for elastohydrodynamic cavity flow. Proc Roy Soc London Series A 400 (1985) 289-313
29. Kemp L. Study of Nordgren's equation of hydraulic fracturing. SPE Prod Engng August (1990) 311-314 [SPE 18959]
30. Murdoch L.C., and Germanovitch L.N. Analysis of a deformable fracture in permeable material. Int J Numer Anal Meth Geomech 30 (2006) 529-561
31. Carter ED. Optimum fluid characteristics for fracture extension. In: Howard GC, Fast CR, editors. Drilling and production practices. Tulsa: American Petroleum Institute; 1957. p. 261-70.
32. Carbonell R.S., Desroches J., and Detournay E. A comparison between a semi-analytical and a numerical solution of a two-dimensional hydraulic fracture. Int J Solids Struct 36 31-32 (1999) 4869-4888
33. Garagash D.I., and Detournay E. Plane-strain propagation of a fluid-driven fracture: small toughness solution. ASME J Appl Mech 72 (2005) 916-928
34. Garagash D.I., and Detournay E. The tip region of fluid-driven fracture in an elastic medium. ASME J Appl Mech 67 (2000) 83-192
35. Garagash D.I. Propagation of a plane-strain fluid-driven fracture with a fluid lag: early-time solution. Int J Solids Struct 43 (2006) 5811-5835
36. Garagash D.I. Plane-strain propagation of a fluid-driven fracture during injection and shut-in: asymptotics of large toughness. Engng Fract Mech 73 4 (2006) 456481
37. Lecampion B., and Detournay E. Implicit moving mesh algorithm for the propagation of plane strain hydraulic fracture. Comput Methods Appl Mech Engng 196 49-52 (2007) 4863-4880
38. Adachi JI, Detournay E. Plane-strain propagation of a hydraulic fracture: finite toughness self-similar solution. Int J Solids Struct; in preparation.
39. Bunger A.P., Detournay E., and Garagash D.I. Toughness-dominated hydraulic fracture with leak-off. Int J Fract 134 2 (2005) 175190
40. Garagash DI. Plane-strain propagation of a fluid-driven fracture in a permeable medium: leak-off dominated regime. Int J Solids Struct; submitted for publication.
41. Batchelor G.K. An introduction to fluid dynamics (1967), Cambridge University Press, Cambridge, UK
42. Settari A. A new general model of fluid loss in hydraulic fracturing. Soc Pet Engng J 25 4 (1985) 491-501 [SPE 11625]
43. Muskhelishvili NI. Singular integral equations. New York: Dover Publications Inc.; 1946 [reprint 1992 of translation; 2nd Russian ed.].
44. Sneddon I.N., and Lowengrub M. Crack problems in the classical theory of elasticity (1969), John Wiley & Sons, New York
45. Bueckner H.F. A novel principle for the computation of stress intensity factors. Z Angew Math Mech 50 9 (1970) 529-546
46. Rice J.R. Some remarks on elastic crack-tip stress fields. Int J Solids Struct 8 6 (1972) 751-758
47. Rice J.R. Mathematical analysis in the mechanics of fracture. In: Liebowitz H. (Ed). Fracture, and advanced treatise vol. II (1968), Academic Press, New York 191-311 [chapter 3]
48. Kanninen M.F., and Popelar C.H. Advanced fracture mechanics (1985), Oxford University Press, Oxford, UK
49. Detournay E, Garagash DI. General scaling laws for fluid-driven fractures. Proc Roy Soc London, Ser A; in preparation.
50. Detournay E. Propagation regimes of fluid-driven fractures in impermeable rocks. Int J Geomech 4 1 (2004) 1-11
51. Barenblatt G.I. Scaling, self-similarity and intermediate asymptotics (1996), Cambridge University Press, Cambridge, UK
52. Peirce A.P., and Detournay E. An implicit level set method for modeling hydraulically driven fractures. Comput Methods Appl Mech Engng 197 (2008) 2858-2885
53. Adachi J.I., and Detournay E. Self-similar solution of a plane-strain fracture driven by a power-law fluid. Int J Numer Anal Meth Geomech 26 (2002) 579-604
54. Kevorkian J., and Cole J.D. Multiple scale and singular perturbation methods (1996), Springer, New York
55. Hinch E.J. Perturbation methods (1991), Cambridge University Press, Cambridge, UK [reprint 2000]
56. In: Abramowitz M., and Stegun I.A. (Eds). Handbook of mathematical function with formulas. Graphs and mathematical tables (1972), Dover, New York
57. Crouch S.L., and Starfield A.M. Boundary element methods in solid mechanics (1983), Unwin Hyman, London
58. Hills D.A., Kelly P.A., Dai D.N., and Korsunsky A.M. Solution of crack problems. The distributed dislocation technique (1996), Kluwer, Dordrecth
59. Ramamurthy G, Hujeux J-C. A moving mesh integro-variational formulation applied to hydraulic fracturing. In: Proceedings of the international conference on computer engineering science, vol. 2; 1988.
60. Detournay E., Cheng A.H.-D., and McLennan J.D. A poroelastic PKN hydraulic fracture model based on an explicit moving mesh algorithm. ASME J Energy Res Tech 112 (1990) 224-230
61. Adachi J.I., Detournay E., and Savitski A.A. Simulation of hydraulic fracturing using an explicit moving mesh algorithm. In: Elsworth D., Tinucci J.P., and Heasley K.A. (Eds). Rock mechanics in the national interest - proceedings of the 38th US rock mechanics symposium vol. 1 (2001), Balkema, Washington, DC/Lisse 243-250
62. Desroches J., Detournay E., Lenoach B., Papanastasiou P., Pearson J.R.A., Thiercelin M., et al. The crack tip region in hydraulic fracturing. Proc Roy Soc London Series A 447 (1994) 39-48
63. Lenoach B. The crack tip solution for hydraulic fracturing in a permeable solid. J Mech Phys Solids 43 7 (1995) 1025-1043
64. Detournay E, Adachi JI, Garagash DI. Asymptotic and intermediate asymptotic behavior near the tip of a fluid-driven fracture propagating in a permeable elastic medium. In: Dyskin A, Hu X, Sahouryeh E, editors. Structural integrity and fracture - proceedings of the international conference on structural integrity and fracture. Lisse: Balkema; 2002. p. 9-18.
65. Garagash DI, Detournay E, Adachi JI. Tip solution of a fluid-driven fracture in permeable rock. J Mech Phys Solids; submitted for publication.
66. Detournay E. Fluid and solid singularities at the tip of a fluid-driven fracture. In: Durban D, Pearson JRA, editors. Proceedings of the IUTAM symposium on non-linear singularities in deformation and flow. Dordrecht: Kluwer Academic Publishers; 1999. p. 27-42.
67. Adachi JI. Fluid-driven fracture in permeable rock. PhD thesis. Minneapolis: University of Minnesota; 2001.
68. Szegö G. Orthogonal polynomials (1939), American Mathematical Society, New York
69. Patankar S.V. Numerical heat transfer and fluid flow (1980), Hemisphere, Washington, DC
70. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical recipes in Fortran, vol. 90, 2nd ed. Cambridge, UK: Cambridge University Press; 1996.